The nature and laws of chance / By Thomas Simpson.

  • Simpson, Thomas, 1710-1761.
Date:
1740
Catalogue details

Licence: Public Domain Mark

Credit: The nature and laws of chance / By Thomas Simpson. Source: Wellcome Collection.

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    aforenamed Problem) : And therefore a a— i a—2 , * . b b—1 b— 2 * \ . v -x-—-x-- (p) m.-x-x- / j 2 2 1 f- f rv 3 C C—I C—2 , . x—— x— (r) n n— 1 n—2 n—3 n—4 ^—$ -x-- x-x--x--x—— 1 2 3 4 5 6 (^) muft confequently be the Value. E. I. COROLLARY I. He nce if the Number of Things of each Sort be equal, and thole propofed to be taken of each alfo equal, and w be put for the Number of Sorts, the Probability, it is manifeft, will become COROLLARY II. When there are only two Sorts of Things, then cyd, r, x, &c. become =0, a+b=nyp+q=my and a a—1 a—2 /.v . b b—1 b—2 , v -x-x- (/) in, -x-x— (q) 12 3 1 2 3 n n—1 n—2 n—3 equal to the required —X* 1 2 •X (m) 3 4 Value in that Cafe; which, when it is propofed that no one of the firft two Sorts fliall be taken, will become ^ ^_j Jy 2 b_2 j -x--x--x-- (m), becaufe then p is =0, and n n—1 n—2 ^-*-3 EXAMPLE I. Jfc. In a Lottery confifting of pp Tickets, whereof there are two Prizes of 1000/. and five of 100/. What is the Pro-